Converting Fractions to Decimals and Order of Operations   Converting Fractions to Decimals To convert fractions to decimals we just divide.  The only catch is when should we stop.  Sometimes we end when there is no remainder. Example Convert the fraction 3/8 to a decimal. Solution              0.375         8 | 3.000                24                        60                       56                     40                     40                    0 Hence                  3                    =  0.375                               8 Other times the digit repeats itself Example Convert the fraction 5/6 to a decimal. Solution              0.833         6 | 5.000                48                        20                       18                     20                     18                    20 We see that if we keep working it out we will continually get 3.  That is                    5                    =  0.833333...                               6 We put a bar over the 3 to indicate that the 3 repeats. 0.83333...  =  0.83  Example Convert the fraction 4 2/7 to a decimal. Solution Divide only the fractional part              0.285714         7 | 2.00000000                14                        60                       56                     40                     35                    50                    49                      10                        7                        30                        28                          20        We are back to where we began. Hence                      2          4          =  .285714Notice the 4 from the mixed number is the whole number part.                             7 Example Fill in the green blank with "<" , ">", or "="            2                                     0.133           15            Solution We first convert the fraction into a decimal.  Then compare.  We will need to divide until we recognize a difference or recognize equality               0.13         15 | 2.00                  15                          50                         45                        50    We see that this is the repeating decimal          0.13   =  0.133333...  Now notice that          0.133 = 0.133000000... < 0.1333333... Exercises Convert the following fractions to decimals 3/4        8 5/9        7  2/11          Order of Operations Just as with whole numbers and fractions the order of operations is: Inside parentheses Exponents Multiplication and Division    For a tie go left first Addition and Subtraction        For a tie go left first Example Calculate         (2.1 - 1)2 + 5.6 x 4 Solution         (2.1 - 1)2 + 5.6 x 4         =  (1.1)2 + 5.6 x 4         =  1.21 + 5.6 x 4        (1.1)2  =  1.1 x 1.1  =  1.21         =  1.21 + 22.4        5.6 x 4  =  22.4         =  23.61 Exercise Calculate         (5 - 2.3) ÷ 0.12 + 3.2 x 0.5     Application Your drill bit is 3/16 inches in radius, but the screw that is to go into the hole is supposed to be 0.2 inches in radius.  How much bigger is the screw then the hole? Solution We convert 3/16 to a decimal.                0.1875         16 | 3.0000                     16                         140                        128                      120                     112                       80                       80                         0 Finding how much bigger is a subtraction problem               199           0.20010       -   0.1875            0.0125 The radius of the screw is 0.0125 inches bigger than the radius of the hole.   Back to the Decimals page Back to the Math 187A page Back to the Math Department page e-mail Questions and Suggestions